Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+9y &= 9 \\ 5x+6y &= 6\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $5x = -6y+6$ Divide both sides by $5$ to isolate $x$ $x = {-\dfrac{6}{5}y + \dfrac{6}{5}}$ Substitute this expression for $x$ in the first equation. $-5({-\dfrac{6}{5}y + \dfrac{6}{5}}) + 9y = 9$ $6y - 6 + 9y = 9$ Simplify by combining terms, then solve for $y$ $15y - 6 = 9$ $15y = 15$ $y = 1$ Substitute $1$ for $y$ in the top equation. $-5x+9( 1) = 9$ $-5x+9 = 9$ $-5x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = 1$.